I have been attempting a question about noisy linear dynamical systems lately. Specifically, suppose we are given a linear dynamical system
$$
x_t = Ax_{t - 1} + \mathcal{N}(0, \sigma^2)
$$
where $A$ is orthogonal, $x_t \in \mathbb{R}^n$, and $\mathcal{N}(0, \sigma^2)$ is a normal distribution...